David knew he made a mistake when he calculated that Gilda walks 123 miles to the station. Read through David's calculations: Using d = rt, the distance is the same, but the rate and time are different. If Gilda misses the train, it means the time t needs 7 more minutes at a rate of 3 mph, so d = 3 (t + 7). If she gets to the station 5 minutes early it means the time t can be 5 minutes less at a rate of 4 mph so d = 4 (t - 5).

3 (t + 7) = 4 (t - 5)

3t + 21 = 4t - 20

t = 41

d = rt, so d = 3 (41) = 123

Find David's mistake in his calculations. In two or more complete sentences, explain his mistake. Include the correct calculations and solutions in your answer.

Question

Dutches

Mathematics

22 March, 20:45

David knew he made a mistake when he calculated that Gilda walks 123 miles to the station. Read through David's calculations: Using d = rt, the distance is the same, but the rate and time are different. If Gilda misses the train, it means the time t needs 7 more minutes at a rate of 3 mph, so d = 3 (t + 7). If she gets to the station 5 minutes early it means the time t can be 5 minutes less at a rate of 4 mph so d = 4 (t - 5).

3 (t + 7) = 4 (t - 5)

3t + 21 = 4t - 20

t = 41

d = rt, so d = 3 (41) = 123

Find David's mistake in his calculations. In two or more complete sentences, explain his mistake. Include the correct calculations and solutions in your answer.

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Answers (1)

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Mario Allison · Answer 1

d = 3 (t + 7) ... (1)

d = 4 (t - 5) ... (2)

3 (t + 7) = 4 (t - 5)

3t + 21 = 4t - 20

t = 41

For finding the Distance to the station, we need to use either equation (1) or (2). Here two different rates are given 3 mph and 4 mph. So, we can't consider r = 3 only.

If we use the equation (1), then

d = 3 (t + 7)

d = 3 (41 + 7)

d = 3 (48) = 144

We can also use the equation (2)

d = 4 (t - 5)

d = 4 (41 - 5)

d = 4 (36) = 144

So, the correct distance to the station is 144 miles.